Question

triangle PQR, from S and T altitudes TQ and SR are drawn, which of the following is true?​

Answer 1

Given: The triangle PQR, from S and T altitudes TQ and SR are drawn.

To find: The correct option of the following.

Solution:

Since TQ and SR are the altitudes from S and T, respectively, the angles RTQ and QSR form right angles. In the triangles RTQ and QSR, The side QR is common, the angles ∠S and ∠T are equal as they are 90°. Because one side and its opposite angle in both the triangles are the same, the angles ∠Q and ∠R are also equal.

So, it can be said that the triangle RSQ is similar to the triangle RTQ by the ASA (Angle-Side-Angle) postulate.

Therefore, option (b) ΔRSQ ~ ΔRTQ is the correct option.